Calculate the Q-value in the following decays:
(a) `^19 O rarr ^19 F + e + vec v`.
(b) `^25 A1 rarr ^25 Mg + e^+ + v`.
The atomic masses needed are as follows :
`^19 O 19.003576 u`
`^19 F 18.998403 u`
`^25 A1 24.990432 u`
`^25 Mg 24.985839 u`

Explanation

(a) The `Q`-value of `beta^(-)` decay is
`= [m(.^(19)O)-m(.^(19)F)]c^(2)`
`=[19.003576u-18.998403 u](931 MeV//u)`
`=4.816 MeV`
(b) The `Q`-value of `beta^(+)`-decay is
`Q=[m(.^(25)Al)-m(.^(25)Mg)-2m_(e )]c^(2)`
`=[24.99032u-24.985839u-2xx0.511(MeV)/(c^(2)]c^(2)`
`=(0.004593u)(931MeV//u)-1.022 MeV`
`=4.276 MeV-1.022 MeV=3.254 MeV.`